Understanding Ellipses

The video tutorial explains how to find the standard equation of an ellipse with given foci and minor axis length. It covers the two forms of ellipse equations based on the orientation of the major axis, either vertical or horizontal. The tutorial guides viewers through graphing the ellipse on a coordinate plane, calculating necessary parameters like B and C, and deriving the final equation using A squared, B squared, and C squared. The video concludes with finalizing the graph by identifying the endpoints of the major axis.

What are the two possible orientations for the major axis of an ellipse?

• Horizontal and vertical

• Diagonal and horizontal

• Vertical and diagonal

• Circular and elliptical

In an ellipse, what is the relationship between the lengths of the major and minor axes?

• The major axis is always shorter

• Both axes are always equal

• The major axis is always longer

• The minor axis is always longer

Where is the center of the ellipse located in relation to its foci?

• At the origin

• Outside the foci

• Halfway between the foci

• At one of the foci

If the distance from the center to the foci is 4 units, what is the value of c?

• 2

• 5

• 3

• 4

How do you calculate a squared in the equation of an ellipse?

• a squared = b squared * c squared

• a squared = c squared - b squared

• a squared = b squared + c squared

• a squared = b squared - c squared

What is the value of a if a squared equals 25?

• 6

• 3

• 5

• 4

What is the equation of the ellipse if a squared is 25 and b squared is 9?

• x^2/25 + y^2/9 = 1

• x^2/9 + y^2/25 = 1

• x^2/16 + y^2/9 = 1

• x^2/25 + y^2/16 = 1

What is the length of the minor axis if b equals 3?

• 9 units

• 6 units

• 12 units

• 3 units

How far are the endpoints of the major axis from the center if a equals 5?

• 5 units

• 4 units

• 6 units

• 3 units

What is the significance of the larger denominator in the ellipse equation?

• It determines the length of the minor axis

• It indicates the orientation of the major axis

• It is always under the y part of the equation

• It is always under the x part of the equation